There are many instances of biological data or signals that are by nature nonstationary, e.g., EEG and ECG. Often the goal is to analyze the data or to evaluate the data quantitatively. Because of the data's nonstationary nature, their existence at various size scales, and the desire to locate features in a computationally efficient way, it is important that we use the wavelet transform to process the data appropriately. This transform has the advantage of representing the frequency content of the data and the time at which they occurred. Moreover, the wavelet transform has the ability to extract features at various scales, to enhance edges, and to zoom in on singularities. We have applied the wavelet transform to the analysis of EEG signals and to the detection of spikes, oscillations, and the onset of seizures. We are currently investigating its use in estimating the fractal dimension of glial nerve cells, to quantitatively measure morphological complexity.